Field of the Invention
The present invention relates to Optical Fast Fourier Transform (OFFT) On Chip design.
Background of the Related Art
Fast Fourier Transform (FFT) has a widespread usage in data and single processing applications such as convolutions, filtering, image processing and data-communication. For instance, the functional analysis of convolution has widespread applications in numerical linear algebra, computer vision, language- image- and signal processing, and neural networks. Discrete convolution is defined for functions on the set of integers, which can be represented with the residue number system (RNS). Conceptually, RNS enables dimensionality reduction of an arithmetic problem by representing a large number as a set of smaller integers, where the number is decomposed by prime number factorization using the moduli as basis functions. These reduced problem sets can then be processed independently and in parallel, thus improving computational efficiency and speed. A second example is the field of convolutional neural networks (CNNs).
A CNN is neural network where instead of fully connecting each input to each output with weights, convolutional filtering connects the network in a spatially local manner. See A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” in Advances in Neural Information Processing Systems vol. 25, F. Pereira et al, Ed. Curran Associates, Inc, 2012, pp. 1097-1105. This convolutional filtering is normally performed by Graphics Processing Units (GPUs). The GPUs convert the input data to the frequency domain with a forward FFT where it is multiplied by a kernel and then converted back into the spatial domain with an inverse FFT. By using OFFTs for convolution instead GPUs, a system can be built to take advantage of the energy efficient arithmetic of wave interference to perform the convolutions of the CNN.
A third application is Orthogonal Frequency Division Multiplexing (OFDM) is a process of encoding digital data on multiple carrier frequencies, which has various applications including for transmission of information such as digital television and audio broadcasting. Fast Fourier Transform (FFT) is widely used as the core process for optical OFDM transmission because of its demonstrably favorable high speed and long-haul data transmission including its high spectral efficiency. See Hillerkuss, D. et al. 26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing, Nature Photon. 5, 364-371 (2011) (“Hillerkuss 1”); Hillerkuss, D., Winter, M., Teschke, M., Marculescu, A., Li, J., Sigurdsson, G., . . . Leuthold, J. (2010), Simple all-optical FFT scheme enabling Tbit/s real-time signal processing. Optics Express, 18(9), 9324, doi:10.1364/oe.18.00932 (“Hillerkus 2”); D. Hillerkuss, A. Marculescu, J. Li, M. Teschke, G. Sigurdsson, K. Worms, S. Ben-Ezra, N. Narkiss, W. Freude and J. Leuthold, “Novel Optical Fast Fourier Transform Scheme Enabling Real-Time OFDM Processing at 392 Gbit/s and beyond,” pp. OWW3, 2010/03/21 (“Hillerkuss 3”).
Previous research studies in the area of OFFT indicate that such technique can be performed at speeds far beyond the limits of electronic digital processing with negligible energy consumption. However, a temporal FFT integrated in photonic has not been realized, nor designed and optimized. Many of the signal processing applications depend on electronic devices which present a bottleneck to provide higher capacity and lower cost implementations. Hence the maximum processing capacity is limited by the speed and the power consumption. See Hillerkuss 2, 3.
The demand for faster communication and computation is rapidly increasing, and driven by emerging industries such as autonomous vehicles, video streaming, mobile, but most importantly data-analytics. New services such as cloud computing and future optical co-processors require high capacity (possibly optical) data processors, co-processors, and accelerators that can perform mathematical functions in parallel since the electrical counterparts are limited by energy, bandwidth, and speed. OFFT benefits information processing by its high bandwidth and Tbit/sec operating speed. Many have approached this challenge by means of different FFT algorithms. However this is not a fully optimized approach since it lacks a sensitivity analysis on the system level in terms of stability, performance, and footprint at the component level.